A relation contains the points (1, -4), (3, 2), (4, -3), (x, 7), and (-4, 6). For which values of x will the relation be a function?
Answers
In response to the stated question, we may state that To conclude, the function problem's relation is a function for all x values except x between 3 and 4.
what is function?In mathematics, a function is a connection between two sets of numbers in which each member of the first set (known as the domain) corresponds to a single element in the second set (called the range). In other words, a function takes inputs from one set and produces outputs from another. Inputs are commonly represented by the variable x, whereas outputs are represented by the variable y. A function can be described using an equation or a graph. The equation y = 2x + 1 represents a linear function in which each value of x yields a distinct value of y.
If and only if each input has precisely one output, a relation is a function. To determine whether the connection stated in the issue is a function, we must examine whether any x values have more than one output.
We may achieve this by putting the specified points on a graph and looking for vertical lines that cross the graph more than once. If so, the relationship is not a function.
We may create the following graph with the supplied points:
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8 |
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7 | ●
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6 | ●
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5 |
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4 | ●
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3 | ●
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2 | ●
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1 |
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0 |
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-1 |
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-2 |
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-3 |
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-4 |
|
|_____________________
-4 -3 -2 -1 0 1 2 3 4
Apart for the line travelling through the points (3, 2) and (4, 2), there is no vertical line that intersects the graph in more than one spot (4, -3). As a result, if x is between 3 and 4, the relation specified in the issue is not a function.
To conclude, the problem's relation is a function for all x values except x between 3 and 4.
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Related Questions
A 0.625 kg basketball is dropped from a height of 3 meters straight down. The coefficient of restitution between the ball and the ground is e = 0.87. At 0.15 seconds after the basketball is dropped, a 58.5 gram tennis ball is dropped from the same 3 meter height straight onto the basketball. If the coefficient of restitution between the tennis ball and the basketball is e = 0.9, determine how high the tennis ball bounces above the ground after the collision. Neglect the size of the balls. (Balls meet at 0.5073 m above ground, final height of tennis ball = 12.6 m above the ground)
Answers
Given that a 0.625 kg basketball is dropped from a height of 3 meters straight down. The coefficient of restitution between the ball and the ground is e = 0.87. At 0.15 seconds after the basketball is dropped, a 58.5-gram tennis ball is dropped from the same 3-meter height straight onto the basketball. If the coefficient of restitution between the tennis ball and the basketball is e = 0.9,
determine how high the tennis ball bounces above the ground after the collision. Neglect the size of the balls.
The balls meet at a height of 0.5073 m above the ground. Hence the height that the tennis ball bounces above the ground is to be calculated.
Given that the coefficient of restitution between the ball and the ground is e = 0.87The coefficient of restitution between the tennis ball and the basketball is e = 0.9
The coefficient of restitution(e) is defined as the ratio of the relative velocity of separation and relative velocity of approach between two objects.
When a ball falls from height, it gains potential energy.
Potential energy (PE) = mghWhere, m = mass of the object, g = acceleration due to gravity, h = height
PE of Basketball = mgh= 0.625 kg * 9.81 m/s² * 3 m= 18.4 Joules
Initial kinetic energy (KE) = PE of Basketball
KE of Basketball = 18.4 J
Let the velocity of the basketball before collision be u1 and the velocity of the tennis ball before collision be u2. After the collision, let the velocity of the basketball be v1 and the velocity of the tennis ball be v2.
Using the coefficient of restitution (e) we can find the velocity of the balls after collision
v1 - v2 = -e(u1 - u2)
Initial momentum (P) = Final momentum (P)
before the collision P = m1u1 + m2u2
after collision P = m1v1 + m2v2P = (0.625 kg * u1) + (0.0585 kg * u2)P
= (0.625 kg * v1) + (0.0585 kg * v2)
Using the above two equations and the given coefficients of restitution, we can find the velocity of the balls after collisionv1 = (m1u1 + m2u2 + e * m2 * (u2 - u1)) / (m1 + m2)v2 = (m1u1 + m2u2 + e * m1 * (u1 - u2)) / (m1 + m2)
Here, m1 = mass of basketball
= 0.625 kg,
m2 = mass of tennis ball
= 0.0585 kg,
u1 = 0, u2 = 0P = m1v1 + m2v2 => v1 + v2 = P / (m1 + m2)
Also given that the time taken by the balls to meet is 0.15 seconds
Let h be the height to which the tennis ball bounces after the collision.
When the tennis ball bounces to height h, it gains potential energy.
KE + PE = Total energy
= Constant Using the principle of conservation of energy we can find the height to which the tennis ball bounces after collision(1/2) * m2 * v2² + (1/2) * m2 * g * h
= (1/2) * m2 * u2² + (1/2) * m2 * g * 0(1/2) * m2 * v2²
= (1/2) * m2 * u2² - (1/2) * m2 * g * h(1/2) * v2²
= (1/2) * u2² - g * h
Substituting the values of u1, u2, m1, m2, e, t and g, we get:
v1 = (0 + 0.0585 kg * 9.81 m/s² + 0.9 * 0.0585 kg * (0 - 0)) / (0.625 kg + 0.0585 kg)v1
= 1.96 m/sv2
= (0.625 kg * 0 + 0 + 0.9 * 0.625 kg * (0 - 0)) / (0.625 kg + 0.0585 kg)v2
= 5.5 m/s
Here, u1 = u2 = 0.
Using the above equation, we can find the height to which the tennis ball bounces after collision (1/2) * (0.0585 kg) * (5.5 m/s)² = (1/2) * (0.0585 kg) * (0 m/s)² - (0.0585 kg) * 9.81 m/s² * h12.83 J
= -0.286 J - 0.572 h0.572 h
= -12.83 J / 2h
= -12.83 J / (2 * 0.572)
= 11.2 m
Hence the height to which the tennis ball bounces above the ground after the collision is 11.2 m.
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DNA on the Ocean Floor (adapted from Baldi book and cont'd from homework 4)- DNA occurs on the ocean floor (outside of living cells) where it plays an important role in nourishing seafloor life. A random sample of ocean floor specimens from 116 locations around the world gives mean sample DNA concentration Xbar=0.2781g/m2 and sample standard deviation s=0.1803g/m2. A healthy concentration of ocean floor DNA is considered to be around 0.31 g/m2.
a. Use the p-value approach to test if the floor specimens mean DNA concentration are different to the what is considered a healthy concentration. Use alpha = 0.05. Start by writing the null and alternative hypothesis. Make sure you write a conclusion regarding the question about the floor specimen's DNA concentration. (1pt)
b. What if the question was: test if the floor specimens mean DNA concentration were less than what is considered a healthy concentration? What would the p- value be? (0.5 pts)
c. Repeat the one-sided test from b. using the 95% confidence interval approach. What do you conclude?
Answers
All parts are define in the below points.
Define the term random sample?A random sample is a subset of a population in which each individual or element in the population has an equal chance of being selected. It is a sampling method used in statistics and research to minimize bias and increase the generalizability of the findings to the larger population.
a. Hypotheses: Null Hypothesis: The mean DNA concentration of the ocean floor specimens is not significantly different from the healthy concentration (µ = 0.31g/m2). Alternative Hypothesis: The mean DNA concentration of the ocean floor specimens is significantly different from the healthy concentration (µ ≠ 0.31g/m2). Using a two-tailed t-test with alpha = 0.05, we find a p-value of 0.0003, which is less than the significance level. Therefore, we reject the null hypothesis and conclude that the mean DNA concentration of the ocean floor specimens is significantly different from the healthy concentration.
b. We would perform a one-tailed t-test with the alternative hypothesis that the mean DNA concentration is less than 0.31g/m2 if the goal was to determine whether the mean DNA concentration of the floor specimens was lower than what is regarded as a healthy concentration. It would have a p-value of 0.00015.
c. Using the 95% confidence interval approach, we construct a one-sided confidence interval for the mean DNA concentration. If the lower bound of the confidence interval is less than 0.31g/m2, we can conclude that the mean DNA concentration is less than the healthy concentration. The 95% confidence interval for the mean is (0.2457g/m2, 0.3105g/m2), which does not include the healthy concentration of 0.31g/m2. Therefore, we can conclude that the mean DNA concentration of the ocean floor specimens is less than the healthy concentration.
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a). We discover a p-value of 0.0003 using a two-tailed t-test with alpha = 0.05, which is below the significance level.
b). Its p-value would be 0.00015.
c). The safe concentration of [tex]0.31g/m^2[/tex] is not included in the 95% confidence interval for the mean, which is [tex](0.2457g/m^2,\ 0.3105g/m^2)[/tex].
Define the term random sample?A random sample is a portion of a community in which every person or component has an equal chance of being chosen. In statistics and research, it is a sampling technique used to reduce bias and improve the generalizability of the results to a broader population.
A). An hypothesis is a The null hypothesis states that there is no discernible difference between the mean DNA concentration of the ocean bottom samples and the healthy concentration [tex](\mu=0.31g/m^2)[/tex]. Alternative Hypothesis: The mean DNA concentration of the ocean floor samples differs considerably from the healthy concentration [tex](\mu\neq 0.31g/m^2)[/tex] in a statistically significant way. We discover a p-value of 0.0003 using a two-tailed t-test with alpha = 0.05, which is below the significance level. We therefore reject the null hypothesis and come to the conclusion that the mean DNA concentration of the samples from the ocean bottom differs significantly from that of healthy individuals.
B). If the objective was to determine whether the mean DNA concentration of the floor specimens was lower than what is considered as a healthy concentration, we would conduct a one-tailed t-test with the alternative hypothesis that the mean DNA concentration is less than [tex]0.31g/m^2[/tex]. Its p-value would be 0.00015.
C). We create a one-sided confidence interval for the mean DNA concentration using the 95% confidence interval method. The mean DNA concentrationis less than the healthy concentration if the lower limit of the confidence interval is less than [tex]0.31g/m^2[/tex]. The safe concentration of [tex]0.31g/m^2[/tex] is not included in the 95% confidence interval for the mean, which is [tex](0.2457g/m^2,\ 0.3105g/m^2)[/tex]. As a result, we can say that the average DNA concentration of the samples from the ocean bottom is lower than the healthy concentration.
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moore's law says that the number of transistors that can be placed inexpensively on a silicon chip doubles every two years. in $1990$, a typical cpu contained about $1,\!000,\!000$ transistors. according to moore's law, how many transistors did a typical cpu contain in the year $2000$?
Answers
According to Moore's Law, the number of transistors that can be placed inexpensively on a silicon chip doubles every two years, a typical CPU contained about 1,000,000 transistors in 1990.
What is the number of transistors in a typical CPU in the year 2000?Let’s first calculate the number of doublings from 1990 to 2000. Number of years from 1990 to 2000 = 2000 - 1990 = 10 yearsDoublings from 1990 to 2000 = [tex]$\dfrac{10 \text{ years}}{2 \text{ years per doubling}} = 5$[/tex] doublingsNow, we can calculate the number of transistors in a typical CPU in the year 2000:
[tex]$$\begin{aligned} \text{Number of transistors in 2000} &= \text{Number of transistors in 1990} \times 2^{\text{number of doublings}} \\ &= 1,\!000,\!000 \times 2^5 \\ &= 32,\!000,\!000 \end{aligned}$$[/tex]
Therefore, a typical CPU contained about 32,000,000 transistors in the year 2000.
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The cost of 2 jackets and 3 dresses is £46. The cost of 2 jackets and 4 dresses is £54. How much does 1 dress cost?
Answers
Answer:
£11
Step-by-step explanation:
Let cost of jackets : x, DRESSES: y.
ATP,
2x+3y = 46 ...(1)
2x + 4y = 54 ...(2)
From 1, we get x = (46-3y)/2
By Substitution in (2), we get:
2(46-3y)/2 +4y = 54
=> 46-3y+4y= 54
=> x = 8
Thus, 1 dress cost: 46-3*8/2 = 46-24/2 =22/2 = £11
Prove that sum of measure of three angles of triangle is 180
Answers
Proved that the sum of measure of three angles of triangle is 180 using the Polygon Angle Sum Theorem
To prove that the sum of the measures of three angles of a triangle is 180 degrees, we can use the Polygon Angle Sum Theorem, which states that the sum of the measures of the interior angles of a polygon with n sides is equal to (n-2) times 180 degrees.
A triangle is a polygon with three sides, so we can apply the Polygon Angle Sum Theorem to a triangle to find the sum of its interior angles. Using n=3, we have:
Sum of measures of interior angles of triangle = (n-2) × 180 degrees
= (3-2) × 180 degrees [since we are dealing with a triangle]
= 1 × 180 degrees
= 180 degrees
Therefore, the sum of the measures of the interior angles of a triangle is 180 degrees. This means that the sum of the measures of the three angles in a triangle is always 180 degrees, regardless of the size or shape of the triangle.
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50 POINTS
A bathroom heater uses 10.5 A of current when connected to a 120. V potential difference. How much power does this heater dissipate?
Remember to identify all data (givens and unknowns), list equations used, show all your work, and include units and the proper number of significant digits to receive full credit
Answers
The power dissipated by the heater is 1260 watts (W).
What is a polynomial?
A polynomial is a mathematical expression consisting of variables (also known as indeterminates) and coefficients, which are combined using only the operations of addition, subtraction, and multiplication.
Given:
Current (I) = 10.5 A
Potential Difference (V) = 120 V
Unknown:
Power (P) = ?
The formula to calculate the power is:
P = VI
Substituting the given values:
P = 120 V × 10.5 A
P = 1260 W
It's important to note that the number of significant digits should be based on the precision of the given values. In this case, both values have three significant digits, so the answer should also have three significant digits. Thus, the final answer should be:
P = 1260 W (rounded to three significant digits).
Therefore, the power dissipated by the heater is 1260 watts (W).
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Jenny works at Sammy's Restaurant and is paid according to the rates in the following
table.
Jenny's weekly wage agreement
Basic wage $600.00
PLUS
$0.90 for each customer served.
In a week when Jenny serves n customers, her weekly wage, W, in dollars, is given by
the formula
W = 600+ 0.90n.
(i) Determine Jenny's weekly wage if she served 230 customers.
(ii) In a good week, Jenny's wage is $1 000.00 or more. What is the LEAST number
of customers that Jenny must serve in order to have a good week?
(iii) At the same restaurant, Shawna is paid a weekly wage of $270.00 plus $1.50 for
each customer she serves.
If W, is Shawna's weekly wage, in dollars, write a formula for calculating Shawna's
weekly wage when she serves m customers.
(iv) In a certain week, Jenny and Shawna received the same wage for serving the same
number of customers.
How many customers did they EACH serve?
Answers
Jenny works at Sammy's Restaurant and is paid according to the rates in the following
table.
Jenny's weekly wage agreement
Basic wage $600.00
PLUS
$0.90 for each customer served.
In a week when Jenny serves n customers, her weekly wage, W, in dollars, is given by
the formula
W = 600+ 0.90n.
(i) Determine Jenny's weekly wage if she served 230 customers.
(ii) In a good week, Jenny's wage is $1 000.00 or more. What is the LEAST number
of customers that Jenny must serve in order to have a good week?
(iii) At the same restaurant, Shawna is paid a weekly wage of $270.00 plus $1.50 for
each customer she serves.
If W, is Shawna's weekly wage, in dollars, write a formula for calculating Shawna's
weekly wage when she serves m customers.
(iv) In a certain week, Jenny and Shawna received the same wage for serving the same
number of customers.
How many customers did they EACH serve?
3 / 3
(i) If Jenny serves 230 customers, her weekly wage is
W = 600 + 0.90n = 600 + 0.90(230) = $807.00
Therefore, Jenny's weekly wage if she serves 230 customers is $807.00.
(ii) We want to find the least number of customers, n, that Jenny must serve in order to earn $1,000 or more. That is,
600 + 0.90n ≥ 1,000
0.90n ≥ 400
n ≥ 444.44
Since n must be a whole number, Jenny must serve at least 445 customers in order to earn $1,000 or more in a week.
(iii) Shawna's weekly wage, W, in dollars, when she serves m customers is given by the formula:
W = 270 + 1.50m
Therefore, Shawna's weekly wage when she serves m customers is $270.00 plus $1.50 for each customer she serves.
(iv) Let's assume that Jenny and Shawna received the same wage, W, for serving the same number of customers, x. Then we have:
Jenny's wage = 600 + 0.90x
Shawna's wage = 270 + 1.50x
Setting these two expressions equal to each other, we get:
600 + 0.90x = 270 + 1.50x
330 = 0.60x
x = 550
Therefore, Jenny and Shawna each served 550 customers.
Q2 NEED HELP PLEASE HELP
Answers
Answer:
The skydiver has an initial height of 3600.
Step-by-step explanation:
3600 is the y-intercept in the form y=mx+b
In the point (0,3600) .Time is the x-axis and Height is the y-axis.
Replacing,
3600= m(0)+b
b=3600
Taking another point: (2, 3536)
We apply the formula to obtain the slope.
m= (y2-y1) / (x2-x1)
m= (3536 - 3600) / (2-0)
m= -64 / 2
m= -32
Joining all the terms:
y=-32x+3600
Find the radius of the sphere with the given volume
V=4500 mm^3
Answers
Answer:
10.24
Step-by-step explanation:
i used an online calculator
Assume that the firm for which you work faces a demand function given by:
P=20-2Q
and a total cost function:
TC=100-2Q^3-100Q+34Q^2
a) Find the profit maximizing level of output (Q)
b) What price should you charge for your product?
c) Based on your answers in the previous two questions, how much profit is this firm making at the profit maximizing level of output?
Answers
The profit-maximizing output of 1.91, the firm is incurring a loss of $29.42.
a) Find the profit-maximizing level of output (Q)To determine the profit-maximizing level of output, we must calculate the marginal cost and marginal revenue of the firm.MC= dTC/dQ= -6Q^2-100+68Q=2(17Q^2-34Q-50)So, the marginal cost of the firm is MC= 2(17Q^2-34Q-50)To find the marginal revenue (MR) we must differentiate the revenue function with respect to Q.MR= dTR/dQ= P + Q(dP/dQ)= 20-4QHence, the marginal revenue is MR= 20-4QAt the point of maximum profit, marginal cost (MC) equals marginal revenue (MR).Therefore, 2(17Q^2-34Q-50)=20-4Q34Q^2-68Q-100=0Solving the above equation gives Q=1.91Therefore, the profit-maximizing output is 1.91 units.b) What price should you charge for your product?The price the firm should charge for its product is given by the demand function, P=20-2Q.Substituting Q=1.91 into the demand function,P= 20-2(1.91) = $16.18c) Based on your answers in the previous two questions, how much profit is this firm making at the profit-maximizing level of output?The total profit of the firm is given by the difference between the revenue and the total cost.TR= P x Q = 16.18 x 1.91 = $30.92TC= 100-2(1.91)^3-100(1.91)+34(1.91)^2 = $60.34Profit = TR- TC= $30.92-$60.34= -$29.42At the profit-maximizing output of 1.91, the firm is incurring a loss of $29.42.
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Charles is 10 years old what is the best estimate of the length of his shoe
Answers
Answer:
Size 3 ♀️
Step-by-step explanation:
In the US, the average shoe size for 10-Year-Old is USA Size 3.
-Jul 12, 2020
What is the intercept value in a multiple linear regression? A. Value of Y when all value of all input variables are zero B. Point where are all X variables intercept on Y axis C. Point where all X variables intercept with each other D. All of above
Answers
The intercept value in multiple linear regression is the value of Y when all the values of all input variables are zero. i.e., option (A) is correct
What is multiple linear regression?Multiple linear regression (MLR) is a statistical technique that determines the relationship between two or more independent variables and a single dependent variable. MLR is a statistical technique that is more general than simple linear regression, which can only handle two variables.
Why is the intercept value important in multiple linear regression (MLR)?The intercept term is critical in Multiple linear regression (MLR) models since it represents the value of the dependent variable when all independent variables are equal to zero, indicating the baseline value of the dependent variable. It also influences the slope of the regression equation because its slope varies across different regression coefficients.
The intercept value is used to calculate the predictions for Y based on various combinations of X values in the model. When all independent variables are equal to zero, the intercept value is equivalent to the constant term or bias term in the model equation.
Therefore, Option (A) is correct, it is critical to have a solid understanding of the intercept value and its interpretation when working with Multiple linear regression (MLR) models.
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6. 4 The point Q (3, -1) has been translated from P by the vector (3) What are the coordinates of the point P?
Answers
The coordinates of the point P is (-1,2) .
What is translation?
In mathematics, a translation is a geometric transformation that moves every point of a figure or a space by the same amount in a given direction. The amount and direction of the movement can be described using a vector, which is a mathematical object that has both magnitude and direction.
Finding the coordinates of the point P :
The coordinates of point P can be found by subtracting the vector from point Q.
To find the coordinates of point P, we need to subtract the vector [tex]\begin{pmatrix}4\\-3\end{pmatrix}[/tex] from the coordinates of point Q, which are (3, -1).
Subtracting the x-coordinate of the vector from the x-coordinate of point Q gives us:
3 - 4 = -1
Similarly, subtracting the y-coordinate of the vector from the y-coordinate of point Q gives us:
-1 - (-3) = 2
Therefore, the coordinates of point P are (-1, 2).
So, the correct answer is (C) (-1, 2).
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A) A resistor has a resistance 1.5 ohm and a voltage 6.00 V across it. What is the current in the resistor? What power does it dissipate? Show your work.B) If the resistor above is immersed in water, how much energy does it deliver to the water in 350 seconds? Express answer in joules and in calories. Show your work.
Answers
A) Current (I)= 4A and power dissipated is 24W
B) The energy delivers to the water in 350 sec is 2009.57 cal.
We have, Resistance of the resistor, R = 1.5 ohm
The voltage across the resistor, V = 6.00 V
Let the current in the resistor be 'I'
By using Ohms' Law
I = V/R ⇒ 6.00 V / 1.5 ohm ⇒ 4 A
Therefore, the current in the resistor is 4 A.
The power dissipated by the resistor,
P = I²R ⇒ (4 A)² × 1.5 ohm ⇒ 24 W
Therefore, the power dissipated by the resistor is 24 W.
B) The energy delivered to the water by the resistor can be calculated using the formula:
E = P × t,
Where P = Power of the resistor = 24 W
t = Time = 350 seconds
Therefore, the energy delivered to the water by the resistor is:
E = Pt ⇒ 24 W × 350 s ⇒ 8400 J
Now, convert it to calories:
1 calorie = 4.18 J
Therefore, Energy in calories = Energy in joules / 4.18
⇒ 8400 J / 4.18
⇒ 2009.57 cal
Hence, the energy delivered to the water in 350 seconds is 8400 J or 2009.57 cal.
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I need help! Refer to functions n and p. Find the function and write the domain in interval notation.
Answers
Answer:
To find the function of n(p(x)), we substitute p(x) for x in the function n(x):
n(p(x)) = p(x) + 4
n(p(x)) = x^2 + 6x + 4
The domain of p(x) is all real numbers. Therefore, we need to find the domain of n(p(x))
To find the domain of n(p(x)), we need to consider the domain of p(x) that makes n(p(x)) a real number. Since the coefficient of the x^2 term is positive, the graph of the function p(x) is a parabola that opens upwards, which means that it has a minimum value. The minimum value of p(x) occurs at x = -3, where p(-3) = 9 - 18 = -9
Therefore, the range of p(x) is [ -9, ∞ ). To ensure that n(p(x)) is a real number, we need to have p(x) ≥ -4. Therefore, the domain of n(p(x)) is [ -3 - 2√5, -3 + 2√5 ] or ( -∞, -3 - 2√5 ] ∪ [ -3 + 2√5, ∞)
in total how many different player nationalities were included in the confirmed squads by the uefa champions leugue teams which qualified for the knowckout stage of the uefa champions lwague on february 2nd, 2023?
Answers
Answer:
Step22-by-step explanation:
In total, the knockout stage of the UEFA champions league includes players from 79 different nationalities.
What is the UEFA champions league?The UEFA champions league is a very popular soccer tournament played in Europe. This tournament includes 16 different teams in the knockout stage. Some of the most popular teams are Manchester City, Liverpool, Napoli, and Real Madrid.
Moreover, even if there are only 16 teams, the players in them are from many different nationalities. Indeed, this year there are players from 79 different countries.
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∠A = x + 2 and ∠B = 2x + 4. What is the measurement of ∠A
Answers
Answer:
(B) 60 degrees
Step-by-step explanation:
You want the measure of angle A = x+2, given that it forms a linear pair with angle B = 2x+4.
Linear PairThe sum of angles in a linear pair is 180°
A +B = 180
(x +2) +(2x +4) = 180 . . . . use the given expressions
3x +6 = 180 . . . . . . . . . simplify
x +2 = 60 . . . . . . . . . divide by 3. Angle A = x+2 = 60
The measure of angle A is 60 degrees.
Write 2/7 + 1/4 as a sum of two equivalent fractions with the same denominator
Answers
2/7 + 1/4 = 15/28 ≅ 0.5357143
Add: 2/7 + 1/4 = 2 · 4/7 · 4 + 1 · 7/4 · 7 = 8/28 + 7/28 = 8 + 7/28 = 15/28
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(7, 4) = 28. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 4 = 28. In the following intermediate step, it cannot further simplify the fraction result by canceling.In other words - two sevenths plus one quarter is fifteen twenty-eighths.
But for the total it would be 15/28
a researcher is interested in exploring the relationship between calcium intake and weight loss. two different groups, each with 26 dieters, are chosen for the study. group a is required to follow a specific diet and exercise regimen, and also take a 500-mg supplement of calcium each day. group b is required to follow the same diet and exercise regimen, but with no supplemental calcium. after six months on the program, the members of group a had lost a mean of 15.6 pounds with a standard deviation of 1.2 pounds. the members of group b had lost a mean of 10.3 pounds with a standard deviation of 1.9 pounds during the same time period. assume that the population variances are not the same. construct a 90% confidence interval to estimate the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not. let population 1 be the amount of weight lost by group a, who took a 500-mg supplement of calcium each day, and let population 2 be the amount of weight lost by group b, who did not take a calcium supplement. round the endpoints of the interval to one decimal place, if necessary.
Answers
The 90% confidence interval for the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not is: resulting in a confidence interval of (4.337, 6.263) pounds.
To construct a 90% confidence interval to estimate the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not, we can use a two-sample t-test with unequal variances.
The null hypothesis is that the true difference between the mean amounts of weight lost by the two groups is zero, and the alternative hypothesis is that the true difference is not zero.
We can use the following formula to calculate the confidence interval:
CI = (x_1 - x_2) ± tα/2 * √((s_1)²/n_1 + (s_2)²/n_2)
where
x_1 = 15.6 (mean amount of weight lost by group a)
x_2 = 10.3 (mean amount of weight lost by group b)
s_1 = 1.2 (standard deviation of group a)
s_2 = 1.9 (standard deviation of group b)
n_1 = n_2 = 26 (sample size of both groups)
tα/2 = t0.05/2,24 = 1.711 (degrees of freedom = n_1 + n_2 - 2 = 50)
Plugging in the values, we get:
CI = (15.6 - 10.3) ± 1.711 * √(1.2²/26 + 1.9²/26)
CI = 5.3 ± 0.963
CI = (4.337, 6.263)
Therefore, with 90% confidence, we can estimate that the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not is between 4.337 and 6.263 pounds.
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Translate the sentence into an equation.
Eight times the sum of a number and 5 equals 7 .
Answers
Let the number be represented by the variable "x". Then, the sentence can be translated into the following equation:
8(x + 5) = 7
Additional multilly a fraction by whole number use symbls
Answers
Answer:
if it's for 1-6 just put a 1 at the bottom and multiply 8×5 and 1×12 for the first question and if u need to divide do that if your looking for answers I can help you but there's that for now :)
Step-by-step explanation:
The following financial data are for the dental practice of Dr. Ortiz when he began operations in July. Determine the amount that would appear in Dr. Ortiz’s balance sheet.
1. Owes $42,000 to the Sanderson Equipment Company.
2. Has cash balance of $31,000.
3. Has dental supplies $11,300.
4. Owes $13,360 to Galaxy Furniture Supply.
5. Has dental equipment of $57,100.
6. Had office furniture of $20,000.
Answers
By answering the presented question, we may conclude that Sanderson amount Equipment Company owes $42,000 Galaxy Furniture Supply owes $13,360. $55,360 in total liabilities
what is amount ?aggregate attempting to determine the time required, total number or amount. The quantity at sight or under consideration is extremely active. the overall effect, relevance, or import. Principle, interest, or a third accounting are all included. Word forms include amounts, amounting, and amounted. pliable noun A quantity signifies how much there still is, how often you have, the amount you require, or the amount that you get. He needs that quantity of cash to get by.
The following figures would appear on Dr. Ortiz's balance sheet:
Assets:
Cash: $31,000
$11,300 for dental supplies
$57,100 for dental equipment
$20,000 for office furnishings
The total value of the assets is $119,400.
Liabilities:
Sanderson Equipment Company owes $42,000
Galaxy Furniture Supply owes $13,360.
$55,360 in total liabilities
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calculate the value of expression 2x squared - 3x + 1 if x equals to -2
Answers
The value of expression is 15.
Define the term quadratic expression?A quadratic equation is a mathematical expression of the second degree, in which the highest power of the variable is 2. An expression is a mathematical phrase that combines numbers, variables, and mathematical operations to represent a value or a set of values.
It takes the form of ax² + bx + c = 0, where a, b, and c are coefficients, and x is the variable.
Given equation is;
⇒ 2x² - 3x + 1
If x = -2, then the solution of equation will be,
⇒ 2×(-2)² - 3×(-2) + 1
⇒ (2×4) + 6 + 1
⇒ 8 + 6 + 1
⇒ 15
Therefore, the value of expression 2x² - 3x + 1 if x = -2 is 15.
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Students of SOHO Swim Academy are to have extra swim lessons if they cannot swim. The table below
gives Information on students in 4th, 5th & 6th grade.
Complete the table
1) how many students need swim lessons?
2) How many students are in the 5th grade?
3)How many of the 4th graders can
swim?
4) How many student in 5th & 6th
grade cannot swim?
5) How many students attend SOHO
Swim Academy?
6) How many students attend SOHo swim Academy?
7) What percentage of 5h grade student can swim?
8) what percentage of students cannot swim?
Answers
Answer:
1. first, add the amount of people who cannot swim. they need swim lessons.
2. add up the people in 5th grade who can swim and the people who cannot. same with the 4th graders.
4. the students that cannot swim, add up the 5th and 6ths graders that cannot swim.
5. add up all of the SOHO swimmers.
6. subtracts SOHO swimmers from swim academy.
set up an equation like this for #7
total number of students that can swim/ total amount of 5th graders = x/100
use the fraction on the left and multiply it by 100.
same with number 8
Step-by-step explanation:
10) Given below are the average marks of a class in five subjects. Draw a bar graph to represent the data. English: 62; Mathematics: 91; Science: 89; Social Studies: 55; Hindi: 56: After drawing the graph, answer the following questions. (i) Which subject shows the maximum average marks and which shows the minimum? (ii) By how much is the average in English more than the average in Hindi?
Answers
The subject with the maximum average is Mathematics, while the subject with the minimum average is Social studies; moreover, there is a difference of 6 between Hindi and English.
Which subject has the maximum and the minimum average?Based on the graph and the values given about each subject, it can be concluded that the subject with the maximum average is Mathematics which has an average of 91, while the subject with the minimum average is social studies with an average of 55.
What is the difference in average between Hindi and English?English average: 62
Hindi average: 56
62 - 56 = 6
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A cylindrical tin filled with oil has a diameter of 12cm and a height of 14cm. The oil is then poured in rectangular tin 16cm long and 11cm wide. What is the depth of the oil in the tin
Answers
The volume of cylindrical tin is 1584 [tex]cm^3[/tex]. The depth of the oil in the tin is 9cm.
[tex]V_1 =[/tex] VOLUME OF CYLINDRICAL TIN
[tex]= \pi r^2 h[/tex]
[tex]=\frac{22}{7}[/tex] x 6 x 6 x 14
= 44 x 36
= 1584 [tex]cm^3[/tex]
[tex]V_2 =[/tex] VOLUME OF RECTANGULAR TIN
= lbh = 1584
= (16)(11)(h) = 1584
= 176h =1584
= h = 1584 / 176
= h = 9 cm
A cylinder is a three-dimensional shape that consists of a circular base and a curved surface that extends upward to meet at a point known as the apex. The volume of a cylinder is the amount of space occupied by the shape and is given by the formula V = πr²h, Once we have calculated the area of the circular base, we can multiply it by the height of the cylinder to get the volume.
To calculate the volume of a cylinder, we need to know its dimensions, which are the radius and height. The radius is the distance from the center of the circular base to the edge, while the height is the distance between the two circular bases.
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what is 3x = 0.5x2 in standard form
Answers
Answer:
-0.5x[tex]x^{2}[/tex]+3x=0
Step-by-step explanation:
$2$ white balls and $5$ orange balls together weigh $8$ pounds. $6$ white balls and $3$ orange balls together weigh $20$ pounds.
What is the weight of $4$ white balls and $4$ orange balls together, in pounds?
Answers
Let's break this problem down step by step.
First, we can work out the weight of one white ball by subtracting the weight of 6 white and 3 orange balls (20 pounds) from the weight of 2 white and 5 orange balls (8 pounds):
Weight of 1 white ball = 8 - 20 = -12
Next, we can work out the weight of one orange ball by subtracting the weight of 2 white and 5 orange balls (8 pounds) from the weight of 6 white and 3 orange balls (20 pounds):
Weight of 1 orange ball = 20 - 8 = 12
Now that we know how much one white and one orange ball weigh, we can work out the weight of 4 white and 4 orange balls together:
Weight of 4 white and 4 orange balls = (4 x -12) + (4 x 12) = 0
Therefore, the weight of 4 white and 4 orange balls together is 0 pounds.
By solving two given simultaneous equations using algebra, we find that the combined weight of 4 white balls and 4 orange balls is 16 pounds.
Explanation:The subject matter of this question pertains to simultaneous equations. The equations in question are, 2w + 5o = 8 and 6w + 3o = 20, where w stands for the weight of a white ball and o stands for the weight of an orange ball. We can solve these equations to find the individual weights of these balls. After finding these values, we substitute these into a new equation, 4w + 4o, to find the total weight of 4 white and 4 orange balls together. By solving these equations, we find that the weight of 4 white balls and 4 orange balls together is 16 pounds.
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The table above shows the number of cups of sugar and of flour needed to make some cookies. If Alex uses 5 cups of sugar to make cookies, how many cups of flour does he need?
Answers
3
Step-by-step explanation:
you can see the ratio of flour to sugar is 3:1 so for every 3 cups of flour is 1 cup of sugar so if you have 5 sugar cups you must have 3 times that of flour so 5×3=15 so 15 cups
Smallest possible answer.
Answers
The smallest possible values for "a" and "b" that satisfy these conditions are when a = 1 and b = 3. This is because 1 is the smallest factor of 15, and 3 is the smallest multiple of 3.
What is integers?
The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.
Let's call the two unknown numbers as "a" and "b"
Since "a" is a factor of 15, the possible values for "a" are 1, 3, 5, and 15.
Since "b" is a multiple of 3, the possible values for "b" are 3, 6, 9, 12, 15, and so on.
The smallest possible values for "a" and "b" that satisfy these conditions are when a = 1 and b = 3. This is because 1 is the smallest factor of 15, and 3 is the smallest multiple of 3.
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